Simplify to lowest terms. $\dfrac{40}{32}$
Solution: There are several ways to tackle this problem. What is the greatest common factor (GCD) of 40 and 32? $40 = 2\cdot2\cdot2\cdot5$ $32 = 2\cdot2\cdot2\cdot2\cdot2$ $\mbox{GCD}(40, 32) = 2\cdot2\cdot2 = 8$ $\dfrac{40}{32} = \dfrac{5 \cdot 8}{ 4\cdot 8}$ $\hphantom{\dfrac{40}{32}} = \dfrac{5}{4} \cdot \dfrac{8}{8}$ $\hphantom{\dfrac{40}{32}} = \dfrac{5}{4} \cdot 1$ $\hphantom{\dfrac{40}{32}} = \dfrac{5}{4}$ You can also solve this problem by repeatedly breaking the numerator and denominator into common factors. For example: $\dfrac{40}{32}= \dfrac{2\cdot20}{2\cdot16}= \dfrac{2\cdot 2\cdot10}{2\cdot 2\cdot8}= \dfrac{2\cdot 2\cdot 2\cdot5}{2\cdot 2\cdot 2\cdot4}= \dfrac{5}{4}$